Any doubling/halving of frequency constitutes an octave. This is pretty easy to understand if you draw it. Draw a sine wave, then draw another one at 2x the frequency of that one. In this example, you'd fit 2 complete cycles of the higher frequency wave in one cycle of the lower frequency wave. The resulting notes are the same, one octave apart.
Octaves have no set range of frequencies. In lower notes, the difference between 40 and 80 Hz is an octave, but with higher notes, the difference between 1000 and 2000 Hz is an octave.
You're right with your HPF example there.